# Independent Wavefront Multiplexing with Metasurfaces via Non‐Injective Transformation

## TL;DR

This paper introduces a new method for precise and independent wavefront control using metasurfaces, enabling advanced photonic applications.

## Contribution

A novel non-injective transformation approach for independent wavefront multiplexing using two metasurfaces is introduced.

## Key findings

- Ultra-compact OAM sorters were designed with independent channel outputs mapped to 2D positions.
- 10-channel multiplexing was achieved with minimal crosstalk and no post-processing.
- The method enables scalable and precise wavefront manipulation for photonic applications.

## Abstract

Metasurface holography offers a powerful approach for manipulating wavefronts at the nano and micro scale. Extensive research has been conducted to enhance the multiplexing capacity for diverse wavefronts. However, the independence of multiplexed channels is fundamentally restricted in techniques using single‐layer metasurfaces, resulting in unavoidable crosstalk and the need for post‐filtering of the output wavefronts. Here, a universal wavefront multiplexing concept is presented based on non‐injective transformation. By employing joint optimization on two metasurfaces, different channels can be independently designed without any constraints on the output wavefronts. To validate this approach, ultra‐compact orbital angular momentum (OAM) sorters are designed. In these experiments, the output beams from different channels can be independently mapped to 2D positions with high fineness. In another application of wavefront‐multiplexed holography, 10‐channel multiplexing is experimentally achieved with minimal crosstalk and without the need for post‐processing. These results demonstrate the independence between channels enabled by the non‐injective transformation in the method. The precise wavefront control and high multiplexing capacity underscore its potential for scalable wavefront manipulation devices.

In this work, a universal metasurface multiplexing strategy is presented based on non‐injective transformation. By jointly optimizing two metasurfaces, multiplexed channels achieve independent wavefront control, overcoming crosstalk limits of single‐layer designs. Experiments demonstrate ultra‐compact orbital angular momentum (OAM) sorters and 10‐channel holography without post‐processing. This approach enables scalable, precise, and high‐capacity wavefront manipulation for advanced photonic applications.